The formal notice, to be published in the Federal Register on Wednesday, sets rates from 2013 through the end of 2017.
Muzak and Music Choice will have to pay rights holders such as musicians and songwriters 8 percent of gross revenues for 2013 and 8.5 percent for future years.
SiriusXM, which has 24 million subscribers, will pay 9 percent of gross revenues for 2013, and an additional 0.5 percent per year until the company is paying 11 percent of its gross revenues for 2017.
Each rate represents a slight increase from current levels. Music Choice and Muzak currently pay 7.5 percent, and Sirius XM pays 8 percent.
The satellite radio provider, Music Choice and SoundExchange argued the rates throughout 2012, and the judges on the royalty board issued their determinations in January. The rates will be effective upon their publication in the Federal Register.
On Tuesday, SoundExchange reported distributing $117.5 million to recording artists and record labels in the first quarter of 2013.